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We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker-Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of magneto-hydrodynamic (MHD) equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming well as adiabatic compression and several radiative loss mechanisms. We discuss applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium.
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We present the implementation and the first results of cosmic ray (CR) feedback in the Feedback In Realistic Environments (FIRE) simulations. We investigate CR feedback in non-cosmological simulations of dwarf, sub-$Lstar$ starburst, and $Lstar$ galaxies with different propagation models, including advection, isotropic and anisotropic diffusion, and streaming along field lines with different transport coefficients. We simulate CR diffusion and streaming simultaneously in galaxies with high resolution, using a two moment method. We forward-model and compare to observations of $gamma$-ray emission from nearby and starburst galaxies. We reproduce the $gamma$-ray observations of dwarf and $Lstar$ galaxies with constant isotropic diffusion coefficient $kappa sim 3times 10^{29},{rm cm^{2},s^{-1}}$. Advection-only and streaming-only models produce order-of-magnitude too large $gamma$-ray luminosities in dwarf and $Lstar$ galaxies. We show that in models that match the $gamma$-ray observations, most CRs escape low-gas-density galaxies (e.g. dwarfs) before significant collisional losses, while starburst galaxies are CR proton calorimeters. While adiabatic losses can be significant, they occur only after CRs escape galaxies, so they are only of secondary importance for $gamma$-ray emissivities. Models where CRs are ``trapped in the star-forming disk have lower star formation efficiency, but these models are ruled out by $gamma$-ray observations. For models with constant $kappa$ that match the $gamma$-ray observations, CRs form extended halos with scale heights of several kpc to several tens of kpc.
This work has the main objective to provide a detailed investigation of cosmic ray propagation in magnetohydrodynamic turbulent fields generated by forcing the fluid velocity field at large scales. It provides a derivation of the particle mean free path dependences in terms of the turbulence level described by the Alfvenic Mach number and in terms of the particle rigidity. We use an upgrade version of the magnetohydrodynamic code {tt RAMSES} which includes a forcing module and a kinetic module and solve the Lorentz equation for each particle. The simulations are performed using a 3 dimension periodical box in the test-particle and magnetostatic limits. The forcing module is implemented using an Ornstein-Uhlenbeck process. An ensemble average over a large number of particle trajectories is applied to reconstruct the particle mean free paths. We derive the cosmic ray mean free paths in terms of the Alfvenic Mach numbers and particle reduced rigidities in different turbulence forcing geometries. The reduced particle rigidity is $rho=r_L/L$ where $r_L$ is the particle Larmor radius and $L$ is the simulation box length related to the turbulence coherence or injection scale $L_{inj}$ by $L sim 5 L_{inj}$. We have investigated with a special attention compressible and solenoidal forcing geometries. We find that compressible forcing solutions are compatible with the quasi-linear theory or more advanced non-linear theories which predict a rigidity dependence as $rho^{1/2}$ or $rho^{1/3}$. Solenoidal forcing solutions at least at low or moderate Alfvenic numbers are not compatible with the above theoretical expectations and require more refined arguments to be interpreted. It appears especially for Alfvenic Mach numbers close to one that the wandering of field lines controls perpendicular mean free path solutions whatever the forcing geometry.
We propose a machine learning method to investigate the propagation of cosmic rays, based on the precisely measured spectra of primary and secondary nuclei Li, Be, B, C, and O by AMS-02, ACE, and Voyager-1. We train two Convolutional Neural Network machines: one learns how to infer the propagation and source parameters from the energy spectra of cosmic rays, and the other one is similar to the former but with flexibility of learning from the data with added artificial fluctuations. Together with the mock data generated by GALPROP, we find that both machines can properly invert the propagation process and infer the propagation and source parameters reasonably well. This approach can be much more efficient than the traditional Markov Chain Monte Carlo fitting method in deriving the propagation parameters if the users would like to update the confidence intervals with new experimental data. The trained models are also publicly available.
The High Altitude Water Cherenkov (HAWC) telescope recently observed extended emission around the Geminga and PSR~B0656+14 pulsar wind nebulae (PWNe). These observations have been used to estimate cosmic-ray (CR) diffusion coefficients near the PWNe that appear to be more than two orders of magnitude smaller than that typically derived for the interstellar medium from the measured abundances of secondary species in CRs. Two-zone diffusion models have been proposed as a solution to this discrepancy, where the slower diffusion zone (SDZ) is confined to a small region around the PWN. Such models are shown to successfully reproduce the HAWC observations of the Geminga PWN while retaining consistency with other CR data. It is found that the size of the SDZ influences the predicted positron flux and the spectral shape of the extended $gamma$-ray emission at lower energies that can be observed with the {it Fermi} Large Area Telescope ({it Fermi} LAT). If the two observed PWNe are not unique, then it is likely that there are similar pockets of slow diffusion around many CR sources elsewhere in the Milky Way. The consequences of such picture for Galactic CR propagation is explored.
Information on cosmic-ray (CR) composition comes from direct CR measurements while their distribution in the Galaxy is evaluated from observations of their associated diffuse emission in the range from radio to gamma rays. Even though the main interaction processes are identified, more and more precise observations provide an opportunity to study more subtle effects and pose a challenge to the propagation models. GALPROP is a sophisticated CR propagation code that is being developed for about 20 years. It provides a unified framework for interpretations of data from many different types of experiments. It is used for a description of direct CR measurements and associated interstellar emissions (radio to gamma rays), thereby providing important information about CR injection and propagation in the interstellar medium. By accounting for all relevant observables at a time, the GALPROP code brings together theoretical predictions, interpretation of the most recent observations, and helps to reveal the signatures of new phenomena. In this paper we review latest applications of GALPROP and address ongoing and near future improvements. We are discussing effects of different propagation models, and of the transition from cylindrically symmetrical models to a proper 3D description of the components of the interstellar medium and the source distribution.
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